Vertical Structure of Disk Galaxies and Their Dark Matter

Vertical Structure of Disk Galaxies and

Their Dark Matter Halos

Arunima BanerjeeDepartment of Physics, IISc

Collaborators

Chanda Jog, Lynn Matthews, Elias Brinks & Ioannis Bagetakos

18 October 2011 TIFR, Mumbai 2

1. A general overview of disk galaxies

2. Our theoretical model for a disk galaxy-Gas gravity included self-consistently

3. Applications & Results

Part 1 Dark matter halo shapes from rotation curve & HI thickness data (outer galaxy)

Part 2 Effect of gas gravity on disk vertical structure(inner galaxy)

4. Summary

5. Future Research

Plan of the talk


NGC 891 – A spiral galaxy, seen edge-on

NGC 628 - a typical spiral galaxy, seen face-on

A general overview of disk galaxies


Building Blocks of a Spiral Galaxy

stars

Gas (HI + H2)

DM Halo

DM Halo


R

z

Pressure Support in the perpendicular plane

Rotation Support in the plane 0 Vrot = 220 km/s

vz(star) = 18 km/s; vz(gas) = 5-8 km/s

The Disk ( Stars + Gas )

RΔ

zΔ

301~

Rz

ΔΔ


Dark Matter HaloV

( R

)

Expected curve for visible disk

R

Observed Rotation Curve

Observed Rotation Curve remains flat with R

Hints at the presence of (unseen) gravitating matter in

the outer galaxy

DARK MATTERDARK MATTER

diskDark Matter

Disk vertical structure also hints at the presence of the dark matter !

18 October 2011 7

Our theoretical model

Vertical hydrostatic equilibrium (i = stars, HI, H2)

(1)

Joint Poisson equation for disk + DM halo

(2)

(3)

( )⎟⎠⎞

⎜⎝⎛

∂∂

−=∂∂><

zzv totali

i

iz ψρρ

2

)(4122

2

DMHHIstotaltotal G

zRR

RRρρρρπ

ψψ+++=

∂

∂+⎟

⎠

⎞⎜⎝

⎛∂

∂∂∂

Eliminating ψtotal between (1) & (2),

( )[ ] ( )22

22

2 114)( 2 rot

i

iDMHHIs

iz

ii vRRz

Gvz ∂

∂−⎟

⎠

⎞⎜⎝

⎛∂∂

++++−><

=∂

∂ ρρ

ρρρρπρρ

observations

Part 1: Known functional form (parameters to be constrained by observed vertical scale height)

Part 2: Known value from mass models (to predict vertical scale height)


( )[ ]2

22

2 14)( 2

⎟⎠

⎞⎜⎝

⎛∂∂

++++−><

=∂

∂z

Gvz

s

sDMHHIs

iz

ss ρρ

ρρρρπρρ

( )[ ]2

22

2 14)( 2

⎟⎠

⎞⎜⎝

⎛∂

∂++++−

><=

∂

∂z

Gvz

HI

HIDMHHIs

iz

HIHI ρρ

ρρρρπρρ

Solution of the equations

( )[ ]2

22

22

22

22 14)( ⎟⎟

⎠

⎞⎜⎜⎝

⎛

∂

∂++++−

><=

∂

∂

zG

vzH

HDMHHIs

iz

HH ρρ

ρρρρπρρ

At each R,

Stars

HI

H2


Part 1 Galactic Dark Matter Halos from Rotation curve and HI scale height data

Applications & Results


Galactic DM halo: Motivation

DM on galactic scales

Galaxy formation and evolution is not clearly understood (cusp/core issue; missing satellite problem)

DM halo shape

-stability of spiral arms and warps-imprints of the galaxy formation and evolution history-constituents particles of DM


Rotation Curve Constraint

DisktotalDM

DMDisktotal

ψψψψψψ−=∴

+=

Rv

Rrottotal2

=∂

∂ψ

From modeling disk luminosity profiles etc

?=∂

∂ztotalψ

V (

R )


R

Observed Rotation Curve

But

Cannot determine the DM halo uniquely!

Traditional Method


The HI scale height constraint

dzdv

z ztotal ρ

ρψ 12 >=<∂

∂

Observed HI scale height CurveSensitive to the vertical-to-

planar axis ratio, and hence the shape of the halo!


DM halo shape & HI thickness

c

ca

c

a a

Spherical (c/a = q = 1) Oblate (c/a = q < 1)

ρDM = M/V = M/4ПqR3

As q , ρDM , h

Prolate (c/a = q > 1)

h h h

Mass enclosed within R from

rotation curve

DM

DM

DM

z = 0z = 0

Assumption: DM halo is spheroidal


Our StrategyV

( R

)


R

Observed Rotation Curve Observed HI scale height Curve

Rtotal

∂∂ψ

ztotal

∂∂ψ

Global constraint on

enclosed mass

Constraint on halo

flattening


Our chosen DM halo profile

p

c

DM

RqzR

zR

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛+

+

=

2

2

22

0

1

),(ρ

ρ

Core density Density index

Core Radius Axis-ratio

De Zeeuw & Pfenniger 1988


Dual Constraints: 3D Gridp = 1, 1.5, 2

{ρ0 , Rc, q}

0ρ

q

cR

{ρ0 , Rc, q}

0ρ

q

cR

1.

2.Fit to the observed rotation curve

Fit to the observed HI scaleheightdata

50,000 grid points to be scanned!

100 grid points to scan

Apply rotation curve constraint

Apply HI scaleheight constraint


Results: Andromeda (M31)

p

cRqzR

zR

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛+

+

=

2

2

22

0

1

),( ρρ

q= 0.4 (oblate)

Banerjee & Jog 2008, ApJ, 685, 254

q = 0.4 lies at the most oblate end of the range of

halo shapes found in cosmological simulations!

Best-fit vs observed HI thickness


Results: Andromeda (M31)…

p

cRqzR

zR

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛+

+

=

2

2

22

0

1

),( ρρ

4 RD

Surface density of the disk components and Dark Matter vs R

DM dominates beyond

~ 3 RD



Results: UGC 7321*

p

cRqzR

zR

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛+

+

=

2

2

22

0

1

),( ρρ

q= 1 (spherical)

Banerjee, Matthews & Jog 2010, NewA, 15, 89*superthin low surface brightness galaxy



Results: UGC 7321* …

p

cRqzR

zR

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛+

+

=

2

2

22

0

1

),( ρρ

~ RD (compact)

Banerjee, Matthews & Jog 2010, NewA, 15, 89

Surface density of the disk components and Dark Matter vs R

DM dominates

just beyond

~ RD


Results: The Galaxy

p

cRqzR

zR

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛+

+

=

2

2

22

0

1

),( ρρ

= 2

= 1 (spherical)

Narayan et al. 2005

But total DM halo mass

small !



Results: The Galaxy…

Banerjee & Jog 2011, ApJL, 732, L8

A progressively more prolate

(i.e q increases with R) DM

halo!

DM halo isodensity contours Best-fit vs observed HI thickness


The DM halo shape can range from being prolate to oblate, and the shape can vary with radius even within R ~ 8 RD

Future Work

What drives the DM halo shapes on galactic scales?

- cosmological merging history ?- Back effect of the baryons ?

Summary & Future Work


The superthin LSB galaxy has a dense compact halo as opposed to the HSB’s.

Future WorkDM halos in superthin dwarf LSB’s dense, compact in general?

If yes,What is the origin of the dense compact halos in the superthindwarf LSB’s and diffuse halos in HSB’s?

Is the superthin stellar disk the reflection of the dense, compact DM halo?

Summary & Future Work…


Part2 Effect of gas gravity on disk vertical structure

Applications & Results


Being a low dispersion component, gas forms a dense layer closer to the midplane & pinches the

layer of stars!

STARS vz(stars) = 18 km/s

GASSTARS

vz(gas) = 8 km/s

Pinching effect of the gas layer


z ( kpc)

ρ sta

rs(z

)

0

At a given R

Sech2 (z/zo) (Theoretical)

Sech(z/z0)

Or

Exp(z/z0)

(Observed)

Steeper density profile

density falls with z more rapidly

pinched layer thickness

The origin of the steep vertical stellar density profile in the Galactic disk


0~

( )[ ] ( )roti

iDMHHIs

iz

ii vRRz

Gvz

22

22

2 114)( 2 ∂

∂−⎟

⎠⎞

⎜⎝⎛∂∂

++++−><

=∂∂ ρ

ρρρρρπρρ

ρDM << ρs + ρHI

taken from a Mass Model

Application of our 3-component Galaxy model

Gas gravity


Results: Steepening effect of gas gravity



Comparison with Observations

3-parameter family of curves suggested by van der Kruit(1988)

)2/(2)( /2/2e

ne

nstars znzSechz ρρ −=

A higher value of n denotes a steeper vertical profile

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

2-2/nSe

ch2/

n (nz/

2ze)

z

n=1 (Sech2)

n=2 (Sech)

n=infinity (exp)


Molecular Ring

Radial variation of ‘n’



HI scale height in dwarf galaxies

DDO 154

NGC 2366HoII

IC 2574


o Gas rich galaxies - Good model for high red-shift galaxies

o Why determine gas scale height?

-Irregular: Observationally un-amenable but crucial in calculating star-formation rates etc

o Our model of gravitationally-coupled stars and gas is ideal to study the dwarf irregulars where gas gravity is comparable with stellar gravity.

Why study dwarf irregulars?


Results

Important implications for star-formation rates in these galaxies!

HI scaleheight vs R Midplane density vsR

Banerjee, Jog, Brinks & Bagetakos 2011, MNRAS, 415, 687


Gas gravity strongly regulates the disk vertical structure

Future Work

-Imprint of Gas Gravity on the Thick Disk

- Effect of gas gravity on DM halo shapes: Prominent at higher redshifts?

Summary & Future Work

Documents

Vertical Structure of Disk Galaxies and Their Dark Matter